Application of the Non-classical Modal Superposition Method in Seismic Analysis of Civil Structures

When performing seismic calculations of civil structures, it is necessary to take into account the effects of the soil structure interaction effect (SSI). At the same time, it is allowed to simulate the soil with impedances from ASCE 4–16, and the civil structure in a geometrically similar way, taking into account the deformation of the foundation slab. However, in the classical modal superposition method, the “ground” damper is not reliably modeled. This is due to the assumption that the damping matrix projected on the basis of eigenvectors has a diagonal appearance, which leads to inaccurate accounting of the energy outflow into the ground during fluctuations of the structure. In view of this, the non-classical modal superposition method is used in this paper, which allows for reliable consideration of the “ground” damper, since the designed damping matrix is taken into account as completely filled. Also in the paper, an approach is presented that takes into account the distribution of equivalent stiffness and damping along the bottom of the foundation slab, which ensures that its flexibility is taken into account. In conclusion, a number of test tasks are presented, demonstrating the advantage of the presented methodology and the accuracy of the results obtained in comparison with calculations using an alternative program. The authors recommend including the non-classical modal superposition method, taking into account the deformation of the foundation slab, in the standards for earthquake resistance of civil structures.